Isotope effects in the vibrational lifetime of hydrogen on germanium(100): theory and experiment

Combining first-principles calculations and sum frequency generation spectroscopy, we elucidate the microscopic details in the relaxation of the stretching vibration of hydrogen adsorbed on Ge(100). The dominant decay channels involve energy transfer from the stretching to the hydrogen bending modes, with the remaining energy difference being transferred to or from substrate phonons. The coupling between stretching and bending modes is treated from first principles using the calculated multidimensional adiabatic potential energy surface, while the coupling to phonons is treated in perturbation theory. For a surface solely saturated with light hydrogen, we calculate a vibrational lifetime of 1.56 ns at 400 K, in good agreement with experiment, and find a similar temperature dependence of the lifetime in both experiment and theory. The calculations show that the stretching energy dissipates to a vibrational state involving four bending quanta of hydrogen, concurrently absorbing a thermally excited surface phonon related to the Ge dimer rocking mode. For a Ge surface saturated with a mixture of H and D, our experiments find that the relaxation rate of the H stretching vibration is markedly increased when compared to a surface saturated with H only. Experimentally, a single decay is observed although H and D atoms will statistically pair on the surface dimers. The vibrational lifetime of the Ge-H stretching mode is up to six times shorter in the presence of adsorbed D atoms. The calculated relaxation rates are consistent with the experimentally observed trend. The theoretical analysis shows that the breaking of symmetry within the Ge surface dimer due to coadsorption of D opens up further relaxation channels that involve absorption or emission of a substrate phonon at various energies. Moreover, the calculations predict an even shorter vibrational lifetime of the Ge-D stretch mode due to efficient coupling to the Ge dimer rocking mode.